A mapping defines transformation of objects from one representation (e.g. raw data or an initial vector space) to another (e.g. a lower dimensional vector space or class labels). There are several types of mappings, fixed mappings, trainable mappings, and special mappings for combining with other mappings or the generation of data. Here they are summarized.
There are five mapping types shortly described in the below table.
C stand for data, usually to be supplied as a dataset or a datafile. Sometimes also matrices of doubles or cell arrays are allowed (see cells and doubles). Fixed mappings are denoted by
F. Trainable mappings show themselves either as untrained (
U) or trained (
G is a generator,
V a combiner and
W an arbitrary mapping.
|C = A*F
F are fully user defined by their parameters. They map data a dataset
A object by object into a different space resulting in a dataset
C. The exact mapping operation does not depend on the data, just on user supplied parameters. An example is the sigmoid mapping W = sigm(,s) which maps all features on the interval [0,1] after applying some scaling defined by
s. Fixed_cell mappings are similar to fixed mappings, but will handle a cell array
A internally. See also cells and doubles.
|T = B*U
|An untrained mapping
U specifies a trainable mapping procedure without supplying the training dataset. By applying it to the training dataset
B it results in a trained mapping
T. An example is the principal component analysis U = pcam(,alf). Classifiers are a special case of trainable mappings
C = A*T
|A trained mapping
T can be considered as a fixed mapping that is optimized for a given training dataset. By applying it to to a dataset
A it maps object by object into another space resulting in a dataset
C. An example is the application of a trained PCA to a new dataset
A resulting in a dataset
C with less features.
W2 = W1*V
V accept as an input another mapping
W1 and combines the two into a new mapping
W2. An example is the routine classc which transforms the outputs of a density based classifier, e.g. parzenc, into posterior probabilities: W = parzenc*classc.
C = A*G
|A generator mapping G generates from a given dataset A a new dataset C in the same space.
cells and doubles
operations: datasets datafiles cells and doubles mappings classifiers stacked parallel sequential dyadic.
user commands: datasets representation classifiers evaluation clustering examples support routines.
introductory examples: Introduction Scatterplots Datasets Datafiles Mappings Classifiers Evaluation Learning curves Feature curves Dimension reduction Combining classifiers Dissimilarities.